Never mind Lutfur Rahman and Tower Hamlets, having elected mayors works.
But only in one condition. That the mayor have one vote in the municipal council. In a system of checks and balances, there is no doubt that the mayor must have the confidence of the municipal council to do anything. Being an elected mayor does not means that you should be above the law.
A recurrent critic of the elected mayor system in the UK is that it lacks oversight as the mayor is running in a way a shadow government. What Lutfur Rahman had done seems serious but he was caught his hand in the cookie jar in a system which helps him.
Local government is a mess in the UK which don’t help the empower the responsability associated with an elected mayor. For example in the specific case of the London boroughs, some boroughs have elected mayors and others have mayors which have no political power. The situation is the same all around the UK. Some major cities have elected mayors and other have not. In Canada and in some parts of the US, cities have become real unitary authorities with boroughs which have very limited powers when they exist. Almost anywhere in the world of local democracy outside the UK, the mayor is an important figure, but in many North American cities, he has one vote like the others in council.
Sadly, akin to the question of unitary authorities which is a ongoing debate which lasted for decades, all local government reforms in the UK had been unfinished business tainted with many cases of NIMBYism and bad compromises. They have created a monster which even have made even the more political citizen become uninterested by all the complexity involved by this framework. With all the districts, counties, metropolitan authories, even an Oxford graduate sometimes have difficulty keeping out the pace.